In celestial mechanics, the Lagrange points ( also Lagrangian points, L-points, or libration points) are orbital points near two large co-orbiting bodies. At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies.
There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L1, L2, L3 are unstable equilibria, whereas L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
For each given combination of co-orbiting planetary bodies there are five Lagrange points L1 to L5 for the Sun–Earth system, and in a similar way there are five different Lagrange points for the Earth–Moon system. Several planets have trojan satellites near their L4 and L5 points with respect to the Sun. Jupiter has more than a million of these trojans. Artificial satellites have been placed in orbits near to L1 and L2 with respect to the Sun and Earth, and with respect to the Earth and the Moon. The Lagrange points have been proposed for uses in space exploration.
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